VII.
GRAVITATION RESEARCH
Academic and Research Staff
Prof. R. Weiss
Dr. D. J. Muehlner
R. L. Benford
Graduate Students
N. A. Pierre
M. Rosenbluh
Margaret A. Frerking
D. K. Owens
RESEARCH
OBJECTIVES AND
SUMMARY OF RESEARCH
The research in this group is in the field broadly labeled experimental relativity.
Our objective is an experimental investigation of the gravitational interaction and the
measurement of cosmological observables.
Specific Projects
1.
Astronomy in the Region 1-0. 1 mm
Our present knowledge concerning the sky in the region between 1 mm and 0. 1 mm
is still very limited. This region of the electromagnetic spectrum includes the cosmic
isotropic background radiation, thermal radiation by interstellar dust, and most likely
discrete sources that are not visible in other regions of the spectrum, in particular, distant sources that may give information concerning the early history of the universe.
Our major effort in this area for the last few years has been to obtain a set of measurements of the spectrum of the isotropic background radiation in the region 3-0.5 mm
In a series of
(3-20 cm-l), using a liquid-helium-cooled balloon-borne radiometer.
Progress
Quarterly
in
(reported
1971
to
September
1969
measurements from September
Report No. 105, pp. 17 -53) we established that the isotropic background radiation follows a Planck distribution appropriate to a blackbody at approximately 2. 7K in
-
-
.
In the region beyond
dominates the specwater,
and
ozone
from
primarily
radiation,
, atmospheric
12 cm
trum even at 40 km altitude.
-1
In an effort to measure the spectrum in the region above 12 cm-1 we made a flight
One of these
in October 1972 at 44 km altitude with a new complement of filters.
filters extends the measurement of the isotropic radiation to 16 cm 1. Two other filters were included to measure the column densities of ozone and water separately. The
results of this flight are still being analyzed, but indications are that the isotropic spec-
the 3-12 cm
1 region.
The blackbody peak occurs at 6 cm
- 1
trum is a Planck distribution up to 16 cm
-l
and that it is indeed the atmosphere that
produces an excess flux for frequencies greater than 16 cm-1
Further measurements of the spectrum from balloon platforms with present infrared technology do not appear to be promising unless we can achieve altitudes of 60 km
This work is supported by the National Aeronautics and Space Administration
(Grant NGR 22-009 -526) and by the Joint Services Electronics Programs (U. S. Army,
U. S. Navy, U. S. Air Force) under Contract DAAB07 -71-C-0300.
QPR No.
108
(VII.
GRAVITATION RESEARCH)
or higher.
These experiments seem to be good candidates for space-shuttle flights.
Our major new effort in far infrared astronomy is a balloon-borne experiment to
measure the isotropy of the background radiation in the spectral region 3-10 cm-1
which includes almost all of the energy of the cosmic background radiation and a minimal
amount of atmospheric radiation. In principle, with a balloon-borne differential radiometer using existing technology, it should be possible to measure .01% anisotropies of the
background radiation in a balloon flight of 2 hours.
The symmetry properties of the expansion of the universe can be determined by
measuring the moments of the intensity distribution of the background radiation. It is
believed that there should be a first moment in the distribution caused by the Earth's
motion relative to the average rest frame of the universe - the co -moving reference
frame. This anisotropy can be characterized by a temperature that is dependent on
the direction of observation
T (1-p2)1/2
T(P, 6) = 1 - p cos e
where p = v/c, v is the velocity of the Earth relative to the frame in which the radiation is isotropic and of temperature T , 6 is the angle between the direction of
observation and the velocity v.
The bandpass from 3-10 cm
- 1
includes almost all of the energy of a 2.7
0
K black-
4
body so that the intensity is given by the Stefan-Boltzmann law: I(T) cc T
The variation in intensity as a function of direction of observation is then of order
I
4p cos 0.
-3
The largest known contribution to p comes from the rotation of the galaxy, P ~ 10 which gives a .04% anisotropy. The proper motion of our local group of galaxies is
unknown, and may be measured in this experiment.
2.
Far Infrared Detection
We are engaged in an experiment to detect far infrared radiation by parametric upconversion in CdS pumped by the 5145 A line of the argon ion laser (see Quarterly Progress Report No. 100, pp. 54-58).
We are also making a study of "hot" electron effects in InSb; specifically, the radiation by hot electrons and the modulation of the far infrared properties of InSb by varying
the electron temperature.
3.
Gravitational Antenna to Search for Gravitational Radiation
from Collapsing Stars and Pulsars
The gravitational antenna is a set of virtually free masses mounted on low-frequency
suspensions that are arranged to form a Michelson interferometer.
Gravitational radiation modulates the separation of the masses. The separation is measured with a null
servomechanism system that maintains the interferometer on a single fringe. A
10-m version of the antenna has a theoretical sensitivity of 10 -21 strain per square root
of detection bandwidth between 30 Hz and 10 kHz.
The principal technological developments accompanying the construction of the antenna are the development of a high-power
argon laser with an amplitude noise approaching the Poisson noise limit and the
design and construction of horizontal suspensions with extremely low mode-mode
QPR No.
108
(VII.
GRAVITATION RESEARCH)
Principal optical components of the antenna are multipass delay
coupling.
including two spherical mirrors, or a corner reflector with a spherical mirror.
4.
lines
Geomagnetic Pulses
An experiment is in progress to search for coincident geomagnetic field fluctuations
-3
over a 100-km baseline which have amplitudes of the order of 10-3 G and rise times less
-1
than 101 s. Events of this nature could be the cause of the signals that J. Weber, at
The instrumentation
the University of Maryland, attributes to gravitational radiation.
is extremely simple. Two 1-m2 induction coils, each with buffer storage, are used
to record the amplitude and rise time of geomagnetic fluctuations that exceed the threshold amplitude of 10 -
4
G in 10 -
1
s or less.
R. Weiss
A.
MEASUREMENT
OF INTRINSIC LASER PHASE NOISE
Joint Services Electronics Programs (Contract DAAB07-71-C-0300)
D. K. Owens
We report a measurement of the phase fluctuations in the oscillation of a gas laser
caused by spontaneous emission.
The phase fluctuations in the signal resulting from the
heterodyne of two independent modes in the laser were measured with the instrument
shown in Fig. VII-1.
The gas laser is a He-Ne laser operating at 1.153 im.
The discharge tube is placed
in an axial magnetic field and, because of the Zeeman effect in neon, the laser oscillates
1-4
An etalon and
at two closely spaced frequencies with opposite circular polarizations.
an iris in the laser cavity limit oscillation to only one longitudinal and one radial mode
for each polarization.
Furthermore, the etalon can be rotated to equalize the cavity
losses for the two circular polarizations.
One of the cavity mirrors is mounted on a
piezoelectric transducer in order to adjust the cavity resonance so that both polarization
modes oscillate with the same intensity.
Under these conditions, and for a sufficiently
strong magnetic field, the difference (beat) frequency between the two oscillating modes
is linearly proportional to the axial magnetic field strength.
The laser is incorporated in a servo system that locks the beat signal 900 out of
phase to an external oscillator by controlling the magnetic field on the discharge tube.
The servo removes low-frequency,
large-amplitude fluctuations in the beat frequency
and permits convenient access through the servo error signal to the laser phase fluctuations.
The laser beam passes through a linear polarizer that converts the two circularly
polarized waves into a linearly polarized wave that is amplitude-modulated at the beat
frequency.
The radiation is detected by a germanium avalanche photodiode cooled to
QPR No. 108
(VII.
GRAVITATION RESEARCH)
200'K.
The photodiode output is amplified by a low-noise,
broadband preamplifier,
squared by a Schmitt trigger and then applied to a phase detector and a frequency discriminator.
The output of the phase detector (point
MAGNET COIL FOR
FARADAY EFFECT
IR IS
7
®
in Fig. VII-1) is proportional
LINEAR
POLARIZER
-DETECTOR
SOLENOID MAGNET
IC
DISCHARGE TUBE
20
PIEZOELECTRIC
TRANSDUCER
Fig. VII-1.
OSC LLATOR
CALIBRATION
Servo system and He-Ne laser.
The length of the laser
cavity
is 107 cm, and the discharge is
IFREOENCY
POWER
FREQUENCY
DISCRIMINATOR
I
AMPLFER
TRIGGER
FLTER
AND
SERVO
COMPENSATION
RECORDER
58 cm long. The mirrors have
a 120-cm radius of curvature.
SCHMITT
AMEL
F FER
LOCK N
AMPLIFIER
TUNED TO w,
PREAMP
LI F
ER
PREAMPLFER
PHASE
DETECTOR
LOCAL
OS CILLA OR
to the phase difference between the beat signal and the local oscillator.
The phase detec-
tor output is the servo error signal that controls the current in the solenoid coil around
the discharge tube.
The frequency discriminator facilitates the phase lock and ceases to
be part of the servo system when the phase lock has been attained.
The power spectrum of the voltage fluctuations measured at
is obtained by using
a lock-in amplifier as a narrow bandpass filter. From these measurements it is possible
to infer the spectrum of the laser phase fluctuations that would be present if the servo
were not used. To do so it is only necessary to note that with respect to phase fluctuations, the servo system is linear and hence can be analyzed in the frequency domain.
Then, at any specific frequency in the closed-loop
voltage at (
configuration, the amplitude of the
is proportional to the amplitude of the open-loop laser phase fluctuation.
The constant of proportionality is frequency-dependent
sinusoidally varying magnetic field to the etalon.
and is obtained by applying a
Because of the Faraday effect in the
etalon glass, the magnetic field produces a time-variant difference in the refractive index
for left and right circularly polarized light. In effect, the cold cavity optical path lengths
for the two polarizations are differentially modulated so that the beat frequency becomes
modulated at the frequency of the time-variant field.
the modulation frequency.
At (
this appears as a signal at
The constant of proportionality is the ratio of the amplitude of
this signal to the amplitude of the open-loop modulation of the beat frequency. The openloop beat-frequency modulation can be measured by varying the magnetic field on the
etalon at a frequency outside the bandwidth of the servo. The signal at 0
is then inde-
pendent of the servo and depends only on the gain of the phase detector and strength of
QPR No.
108
(VII.
GRAVITATION RESEARCH)
the magnetic field on the etalon. These quantities can be measured and the ratio of the
change in beat frequency to magnetic field strength calculated.
This ratio is frequency-
independent and serves to calibrate the instrument at all modulation frequencies. With
this information, we can also determine the Verdet constant of the etalon glass.
5
Figure VII-Z shows the power spectrum of the frequency fluctuations in the beat
signal for output mirror transmittances of 4. 3% and 1. 6%.
In all of these experiments
the beat frequency was 150 kHz, the discharge current was 20 mA, and the laser output
power was kept constant at 6. 4 +. 3 iW per polarization by adjusting the etalon and cavity
mirrors.
8
Fig. VII- 2.
I
Power spectra of the laser frequency fluctuations
for S = 1.65 X 107 photons per
o
+
oRT
and S = 6. 2 X 10
THEORETICAL
MINiMUM
,8
o
The theoretical
T=4.3%
++ I
+++.
photons per mode
minimum
(1. 6% case)
(4. 3% case).
of the power
spectrum
System noise, which is primarily amplitude noise
converted into phase noise in the Schmitt trigger, is
determined by measuring the noise at the mixer
output when the photodiode is illuminated by infrared radiation from an LED amplitude-modulated
at the beat frequency. The photo signals from the
LED and laser are equal.
THEORETICAL
MINIMUM
SYSTEM
NOISE
mode
(determined from Eq. 1) is indicated for each case.
I-.S
-
6
/
/
J/
5
3
102
104
10
v
10
(Hz)
The cavity Q for each case was measured by using an auxiliary 1. 153 jm He-Ne
laser to determine the linewidth of the Fabry-Perot resonances of the laser cavity. The
Q was measured as (9. 9
1) X 10 7 for the 1.6% transmittance case, and (9.7 ±)
for the 4. 3% transmittance case.
Since the power, Q,
X 107
and discharge conditions are
essentially the same for both cases, the only difference is in the radiation density stored
in the laser cavity.
Above 1 kHz, the spectrum appears flat and clearly shows that the frequency fluctuations increase with decreasing radiation density in the cavity. For the 1. 6% transmittance case, the number of stored photons per mode is 1.65 X 107 and the power spectrum
is f (v) = (9.6 ± 2) X 10 2 Hz /Hz; for the 4.3% transmittance case the number of
6
2
-1
2
Below 1 kHz,
Hz /Hz.
stored photons per mode is 6. 2 X 106 and f (v) = (2. 7 ± .3) X 10
the spectrum is dominated by extrinsic sources such as acoustic and ground vibrations.
The data strongly suggest that the frequency fluctuations above 1 kHz are due to spontaneous emission.
QPR No. 108
(VII.
GRAVITATION RESEARCH)
The spectrum of the intrinsic frequency fluctuations of a single-mode laser is given
by
f2 (v) = D
(1)
where D is the intrinsic laser linewidth. 6 ' 7 A lower limit can be placed on D by using
the formula derived by Scully and Lamb 8
1 v
D 2 SQ'
where v is the laser oscillation frequency, S the number of photons stored in the mode,
and Q the quality factor of the laser cavity. The spectrum of the beat-frequency fluctuations is twice that of (1),
provided that the two modes are independent.
With previ-
ously given values of S and Q, we calculate the power spectra to be
4
X 10 -
T = 4.3%
fB(v) = 1.
T = 1. 6%
f (v) = 5. 1 X 10 -
1
Hz2/Hz
Hz /Hz.
The measurements are consistent with theoretically predicted values.
It is possible to measure extremely small Verdet constants with modest fields by
using the technique described in this report.
to have a Verdet constant of 12. 5 X 10 signal-to-noise ratio.
3
For example, the etalon glass was found
min/G-cm, where a field of 1.7 G gave a large
The intrinsic laser phase fluctuations limit our ability to mea-
sure differences of refractive index in transparent materials for right and left circularly polarized light of
f
nR - n L
fT
(v )
Llase
Z L
r
ssample
where T is the integration time.
This technique may find application in the measurement
of electron densities in
tenuous plasmas,
and holds some promise for making a measurement of the refractive
index of strong electric or magnetic fields as predicted by quantum electrodynamics. 9 ' 10
References and Footnotes
1.
2.
P. T. Bolwijn, in P. L. Kelley, B. Lax, and P. E. Tannenwald (Eds.), Proc.
International Conference on the Physics of Quantum Electronics, Puerto Rico,
1965 (McGraw-Hill Book Company, Inc., New York, 1966), p. 620.
M. Sargent III, W. E. Lamb, Jr., and R. L. Fork, Phys. Rev. 164, 436 (1967).
QPR No. 108
(VII.
and R.
L. Fork, Phys. Rev. 164, 450 (1967).
3.
M.
Sargent III, W. E.
4.
R.
Paananen,
5.
In the frequency domain, phase fluctuations and frequency fluctuations are equivalent.
Lamb, Jr.,
GRAVITATION RESEARCH)
C. L. Tang, and H. Statz,
Proc. IEEE 51,
The respective power spectra are related by v2
63 (1963).
(v) = f 2(v).
Amster-
6.
A. Maitland and M. H. Dunn, Laser Physics (North-Holland Publishing Co.,
dam, 1969), p. 288.
7.
W. E. Lamb, Jr., in C. DeWitt, A. Blanding, and C. Cohen-Tannoudja (Eds.),
Quantum Optics and Electronics; Lectures Delivered at Les Houches during the
1964 Session of the Summer School of Theoretical Physics, University of Grenoble
(Gordon and Breach Publishers, Inc., New York, 1965), p. 377. The power spectrum, f2(v),
can be derived from results presented in references 6 and 7.
O. Scully and W. E.
Lamb, Jr.,
Phys. Rev. 159,
208 (1967).
8.
M.
9.
T. Erber, in B. Lax, F. Bitter and R. Mills (Eds.), International Conference on
High Magnetic Fields, Cambridge, Massachusetts, 1961 (The M. I. T. Press, Cambridge, Mass., and John Wiley and Sons, Inc., New York, 1962), p. 706.
10.
R. Baier and P.
QPR No. 108
Brertenlohner, Nuovo Cimento 47B,
117 (1967).